YES

Problem:
 f(x,y) -> h(x,y)
 f(x,y) -> h(y,x)
 h(x,x) -> x

Proof:
 Bounds Processor:
  bound: 1
  enrichment: roof
  automaton:
   final states: {3}
   transitions:
    f0(3,3) -> 3*
    h0(3,3) -> 3*
    h1(3,3) -> 3*
  problem:
   
  Qed